464, Royal Society :— 
In1858, Mr. Dale, in conjunctionwith Dr. J. H.Gladstone, F.R.S., 
presented to the Royal Society* a valuable series of determinations, 
evincing highly interesting results relative to the change of refractive 
power in various substances under different temperatures. 
None of these media being high in the scale, they have little 
bearing on the main object of my inquiries. In two cases (viz. water 
and alcohol) the indices agree so closely with mine, that it was not 
worth while to recalculate them. In two other cases I have carried 
out the numerical comparison, which affords a good agreement with 
the theory. 
Very recently the same gentlemen have, however, published some 
observations on several other media, especially phosphorus, a sub- 
stance at the very summit of the scale, for which I had long been 
extremely desirous to obtain some determinations of indices. 
Among these results only two sets are in a form in which they can 
be made available for comparison with theory. These are the indices 
for the standard rays in bisulphide of carbon, and for solution of phos- 
phorus in that medium, which I have now calculated theoretically. 
The results (given in the sequel) in both cases indicate discre- 
pancies between theory and observation too great to be due to any 
reasonable allowance for error; and we are confirmed in the con- 
clusion before arrived at, that, for highly dispersive substances, the 
theory, IN ITS PRESENT STATE, is defective. 
But these comparisons are all made by means of the same formula 
employed in my former researches, viz. that derived from Cauchy’s 
theory by Sir W. R. Hamilton, which he communicated to me, and 
which I explained in a paper in the Philosophical Magazinef. 
Considering the unsatisfactory condition in which the question 
was left when tried by the test of the higher media in my former 
inquiries, it is a matter of some surprise that in the long interval 
since the publication of those results no mathematician has been in- 
duced to revise the theory. Some criticisms indeed were advanced 
by Mr. Earnshaw§, and others by Prof. Mosotti and the Abbé 
Moigno||, bearing on the general principle. Sir W. R. Hamilton’s 
formula in particular was founded on certain assumptions con- 
fessedly but approximate. It remains then a promising field for 
inquiry to analysts, whether a better formula might not be deduced, 
or other improvements made in the general theory, by which a 
method applying so well to lower cases might be made equally 
successful for the higher. 
Results of calculation, for Ether, Hydrate of Phenyle, Oils of Spike- 
nard, Lavender and Sandal-wood, Benzole, Bisulphide of Carbon, 
and Solution of Phosphorus in that medium. 
Three indices assumed from observation, Viz. ys Hp, and p ai give 
the medium constants, viz. 
Hp Hp 
D!=p,+hy 2p: 
* Phil. Trans. 1858. + See Phil. Mag. July 1859. 
+ Vol. viii. N.S. March 1836. § See Phil. Mag. April 1842 and August 1842. 
|| See British Association Reports, 1849, Sect. Proc. p. 8. 
